GATE XE Complex variables PYQs & Answers

Attempt a question, record the concept and assumptions, then check the available answer. Rework mistakes after revising the relevant concepts. Topic tags can overlap; review the question context.

Questions 1–10 of 11. Imported answers require independent review unless marked reviewed.

Topic practice 11 questionsPage 1 of 2

For the complex function

consider the following two statements

is not analytic at

does not satisfy the Cauchy-Riemann equations along the

-axis.

Then, which one of the following statements is true?

Your answerChoose one option.

P is false and Q is true

P is true and Q is false

Both P and Q are true, and Q implies P

Both P and Q are true, but Q does not imply P

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Let

be an analytic function such that

where

. Then the value of

is equal to

Your answerChoose one option.

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Consider

, where

and

. Which of the following statements is correct?

Your answerChoose one option.

is periodic

is not periodic

for all

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Which one of the following functions is differentiable at

but NOT differentiable at any other point in the complex plane

Your answerChoose one option.

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Let

be the set of complex numbers. Let the function

for

be analytic in

, where

denotes the derivative of

, then

Your answerChoose one option.

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Given that

. The value of

Your answerChoose one option.

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Let

be a complex number. Then the series

Your answerChoose one option.

converges for all

converges for

and diverges for

converges for

and diverges for any

converges for

and diverges for

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Let

, where

is the complex conjugate of

. Then it is differentiable on

Your answerChoose one option.

the entire complex plane

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Let

, where

and

is the circle

oriented counter clockwise. Then, the value of

rounded off to one decimal place is ________ .

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Let

denote the set of complex numbers and

. Let

be the simple positively oriented circle

and

. If

is analytic in

and is given by

then the value of the contour integral

Your answerChoose one option.

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GATE XE Complex variables PYQs

How to practice Complex variables

Question 11

Question 18

Question 18

Question 15

Question 12

Question 3

Question 4

Question 3

Question 11

Question 9